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Compression–bending behavior of a scaled immersion joint
Tunnelling and Underground Space Technology 49 (2015) 426–437
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Compression–bending behavior of a scaled immersion joint Wenhao Xiao a, Haitao Yu b, Yong Yuan c,⇑, Luc Taerwe a,d, Rui Chai e a
Department of Structural Engineering, Ghent University, Ghent, Belgium Key Laboratory of Geotechnical and Underground Engineering (Tongji University) of Ministry of Education, Tongji University, Shanghai 200092, China c State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China d High-End Foreign Expert at Tongji University, Shanghai, China e Hong Kong-Zhuhai-Macao Bridge Authority, Zhuhai 519095, China b
a r t i c l e
i n f o
Article history: Received 8 August 2014 Received in revised form 23 May 2015 Accepted 2 June 2015 Available online 17 June 2015 Keywords: Immersed tunnel Element joint Compressive–bending test Scaled model Stiffness
a b s t r a c t The mechanical behavior of an element joint of an immersed tunnel subjected to quasi-static axial compression and horizontal bending is investigated in this research. To explore the performance of the immersion joint compression–bending loads are applied on a scaled specimen in specific patterns, which are designed based on a practical project. It is found that the extension and closure of the immersion joint vary non-linearly with applied axial forces. Fitting equations for axial stiffness are correspondingly given with regard to loading and unloading states of the joint. Under bending action the element edges which constitute the immersion joint still remain plane. Observed rotations of the joint are non-linearly increasing with bending moment, whether it is pushed forward or bend inversely. Hysteresis behavior obviously exists and the hysteretic loop tends to contract with the increase of the axial force. The stiffness ratio of the joint with respect to that of the tunnel element in service states ranges from 1/360 to 1/120 for the axial stiffness, and from 1/29 to 1/212 for the flexural stiffness. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction An immersed tunnel consists of precast tunnel elements. The tunnel elements are being floated to the construction site and then are immersed in a trench excavated in the bottom of a water way. The immersion joints, which are connecting adjacent elements, are the weakest units in the whole tunnel (Ingerslev, 2010; ITA Working Group 11, 2011). According to the stiffness ratio of the joint to the element, immersion joints can be divided into three categories: rigid joints, flexible joints and partial-rigid (or partialflexible) joints. Akimoto et al. (2002) summarized the types of immersion joint developed in Japan. Whatever the type of immersion joint is, the design of it has to consider various actions during its service life, water pressure, earthquake, settlement of foundation, shock from shipwrecks, and other actions. Meanwhile, an immersion joint should include the water-proof part as an indispensable system. Therefore, knowledge of the deformation of a joint under loading is important for a safe, reliable, and water-proof design. Further, due to the water pressure in the construction phase, the immersion joint is submitted to an initial compression. It is vital to know the behavior of the ⇑ Corresponding author at: R326 Geotechnical Building, Tongji University, 1239 Siping Road, Shanghai 200092, China. E-mail address: [email protected] (Y. Yuan). http://dx.doi.org/10.1016/j.tust.2015.06.002 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
immersion joint after immersion. Therefore, the axial stiffness for this situation is required for calculation and design. Theoretically, the mechanical behavior of an immersion joint was considered under imposed deformation (Liu, 2009) or under seismic action (Anastasopoulos et al., 2007). Yu et al. (2014) deduced a bi-linear formula to account for the stiffness of a flexible joint, which was also verified through numerical modeling. It should be noted that there are not much experimental works reported on immersion joints even though they came to practical applications for more than 100 years. Kiyomiya et al. (1992) performed a quasi-static test for the mechanical properties of a flexible joint with 1/4 geometric scale. In this test the flexural and compression behaviors of a joint were obtained. The results showed that the immersion joint behaved non-linearly in quasistatic and quasi-dynamic cases. Kiyomiya et al. (2004) also carried out both a 3-dimensional experiment and a finite element analysis for a new type of flexible joint referred to as the Crown Seal. Results of both tests indicated that this new type of joint can be applied in practice because of the effective reduction of deformation with this particular design. Hamazaki et al. (1999) applied a new type of steel device to the immersion joint. In these experiments, the axial and transversal mechanical properties of the joint were studied under static, cyclic and eccentric loading. The results showed that this device can play a role in energy dissipation. It can be seen that the behavior of immersion joints was often simplified
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as a bi-linear curve or the stiffness was regarded as a constant, which cannot reflect the real behavior of an immersion joint. However, former researchers mostly dealt with the response of a complete tunnel. Results in the tests done by Kiyomiya et al. (1992) also proved this. Moreover, only a few experiments were found about the flexural mechanical behavior of large-scale immersion joints as well as its flexural stiffness. It should be noted that extension of the immersion joint may be caused from compression and tension due to different types of actions in tunnel elements. The differential extension of the immersion joint may be introduced as ‘‘snake” movement of an immersed tunnel along its longitudinal profile, whether from settlement of foundation or from stratum movement during earthquake (Owen and Scholl, 1981). This paper presents a compression–bending static test of a halfflexible immersion joint with a 1:10 geometric scale. Modeling techniques for the scaled immersion joint were applied. For the experiment on the mechanical behavior of the immersion joint, considering the system model, measurement system and loading patterns, were defined. The compression on the scaled model is applied axially to simulate the water pressure on the immersion joint at typical buried depths. Bending moments are applied cyclically at equal amplitude in the horizontal plane, by varying the load in the axial hydraulic jacks on each sidewall of the element. Through observed load–deformation curves, both the axial stiffness and the flexural stiffness of the joint will be derived for use in practice.
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segmental joints. The cross-sectional dimension of the immersion joint is about 37.95 m 11.40 m (Fig. 2(a)). The partial-flexible immersion joint generally includes a GINA seal, an Omega water proof, shear keys and steel shell shown in Fig. 2. When the immersed tunnel is installed, the GINA seal between elements will be pressed tightly with a minimum compression, resulting in a waterproof sealing due to initial water pressure. The initial water pressure varies from the depth of the immersion joint, resulting in different initial axial force in the joints. Therefore, the purpose of the GINA seal is to seal the immersion joints between two adjacent tunnel elements, ensuring the water tightness of the structure. If the GINA seal fails, the Omega water proof, as the second water tightness defense, will start to work to avoid severe leakage. As a result of earthquake loading and differential settlement, ground motion will cause movement of the immersed tunnel. This movement will result in an extra axial force and a transversal force on the immersion joints (Van Oorsouw, 2010). The force in axial direction works on the cross section of the joint as well as the moment and they will be transferred from one element to another through the GINA seal. Moreover, shear keys are used to transfer transversal forces. Hence, to study the flexural mechanical behavior of the immersion joint, only the GINA seal component is considered in this paper. 2.2. Deformation of immersion joint
2. Background 2.1. Immersion joints As mentioned above, the immersion joints differ in stiffness and in this paper, the half-flexible one is presented. This choice is based on the real project of the Hong Kong–Zhuhai–Macao link which is under construction. The immersed tunnel in this project is approximately 5664 m in length. It consists of 33 elements and is finally connected to two artificial islands, as can be seen in Fig. 1. The length of a typical element is 180 m and is assembled through 8 segments with 22.5 m in length between which are
From the researches by Owen and Scholl (1981), the deformation mode of underground structures subjected to earthquake loading can be divided into three categories: compression/extension, bending and racking. Regarding immersed tunnels, the first two modes dominate the deformation of immersion joint during earthquake. In this study, the effect of longitudinal bending is mainly considered to express flexural mechanical behavior of immersion joints. As can be seen in Fig. 3, when the joint is subjected to axial force, the axial compression d occurs in the joint. If the axial force and bending moment are applied together, the joint is compressed and rotates which means that both compression d and rotation h
Fig. 1. Sketch of immersed tunnel in HZMB (CCCCHZMB, 2011).
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(a) Original profile of immersion joint
(b) Detail view of A-A Fig. 2. Immersion joint in HZMB.
Fig. 3. Compression and bending of immersion joint.
occur. Hence, various loading cases can be considered to analyze this bending deformation by controlling the axial force and bending moment.
3. Scaled model of immersion joint 3.1. Model element of the tunnel The original profile of cross-section of a tunnel element, which was adopted in HZMB, is shown in Fig. 2(a). It consists of two vehicle passages and one gallery serving for emergency. Bending of the immersion joint could happen either in the vertical or horizontal plane. For the consideration of loading, here only horizontal bending will be applied. As the shaped corners in passages and middle walls contribute insignificantly to compression or bending of the joint, the cross-sectional profile of the model element was simplified as rectangular and the middle walls were not considered as Fig. 4(b) and (c) display, compared to the original cross-section.
Furthermore, the shaded parts refer to the horizontal steel shear keys. Based on the capacity of available testing facilities and the goal of the experiment, a geometric scale of 1:10 is selected. The geometric reinforcement ratio for model is the same as that in HZMB. But in the vicinity of the joint, the model element was enhanced. Fig. 4 also provides the dimensions of a single tunnel element with a width of 3800 mm, a height of 1150 mm, and a length of 1250 mm, as well as a 150 mm-thick concrete slab. Referring to the Chinese Code for concrete structure (GB500102010), the types of concrete and reinforcement are C50 and HRB335 respectively. 3.2. Model immersion joint The model immersion joint follows the design of HZMB and the lay-out is also simplified according to the experiment. The steel shell and omega profile are not adopted in this model joint due to the lack of contribution to flexural behavior of the immersion joint.
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(a) Model tunnel
(b) Model Element A
(c) Model Element B
Fig. 4. Cross-section of model immersed tunnel (units: mm).
3.2.1. Steel shear keys In the real immersion joint, shear keys will be situated in walls and slabs as shown in Fig. 2(a). As horizontal seismic loading is considered in this test, vertical shear keys are not provided and also the inner walls have been deleted. However, the horizontal shear keys are design based on the HZMB project with geometric scale of 1:10. With respect to the flexural behavior of the immersion joint in this test, shear keys will not be active during the test. Hence, the behavior of the steel shear keys is not discussed in this paper. 3.2.2. GINA-type seal A certain type of GINA seal is designed and manufactured independently for this experiment. Fig. 5 displays the dimensions of the model GINA profile, and Table 1 lists its physical parameters. Fig. 6 shows the load–compression curves of GINA-type, which is obtained in material test. The loading rate is the same as that in the following test. From the graph it can be seen that the GINA-type seal becomes stiffer when the compression force increases. The variation in slope
(a) Dimension of the model GINA-type (unit:mm)
Table 1 Physical characteristics of the rubber used for the GINA-type seal (provided by producers). Characteristic
Value
Hardness Breaking tenacity Extensibility Allowable compressive strength Shear modulus Friction coefficient
55–60 Shore A 14 MPa >450% 10 MPa 0.98–1.47 MPa Steel:0.2; Concrete:0.3
can partly be attributed to the specific geometry of the GINA-type seal (see Fig. 5) for which the total height of the smaller top part is about 8.5 mm. It also can be seen in Fig. 6 that the behavior of the Trelleborg GINA as used in the HZMB project and the model GINA-type are close to each other. Under the maximum applied load of 2500 kN, the maximum compression of the Trelleborg GINA and the model GINA-type is 19.0 mm and 20.4 mm respectively, with
(b) GINA-type profile
Fig. 5. Dimensions of the model GINA-type profile.
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4.1.3. Measurement lay-out and data acquisition system During the test, in order to figure out the flexural behavior of the immersion joint, the deformation of the joint needs to be monitored. Hence, 5 displacement transducers are placed to accomplish it, which are shown in Fig. 9. The transducers are situated evenly along the joint in order to obtain the distribution of the displacement along the joint as well as its rotation. These displacements are collected by a digital data acquisition system. 4.2. Loading protocol
Fig. 6. Comparison of load–compression curves of Trelleborg GINA and model GINA-type (loading rate: 1 kN/s).
only 7% difference between them. After installation, the detailed and full views of model are shown in Fig. 7.
4. Compression–bending test 4.1. Loading test set-up 4.1.1. Loading system As illustrated in Fig. 8, the tunnel model was placed in a steel loading frame. During a typical experiment, one tunnel element (Model Element A) is fixed horizontally while the other one (Model Element B) is movable, resulting in a deformation of the immersion joint. This test set-up, which is designed by our research group, mainly consists of an axial part and a transversal part in order to meet the demand of the experiment. This reaction frame can provide the following particular functions: (1) One model element inside the frame can have 2 degrees of freedom in the horizontal plane while the other one needs to be fixed in the loading direction. (2) The stiffness of the reaction frame should be much larger than that of the immersion joint. Fig. 8(a) also shows the 4 loading points of the test. In the aforementioned description, the axial forces are applied to Model Element B. Thus, 4 hydraulic jacks are situated between this element and the reaction wall, displayed in Fig. 8. These jacks can only provide pressure to the element but no tension. The axial loading is applied by 4 hydraulic jacks in the end of Model Element B (Fig. 8(b)). By controlling the jacks, different levels of axial forces and bending moment can be applied in the element, which is detailed in next section. In order to figure out the flexural behavior of the immersion joint, this experiment employs a moment reversed quasi-static loading pattern.
4.1.2. Installation of model immersion joint According to the aforementioned loading system, a reaction frame was designed, including axial reaction part and a supporting system. To increase the axial stiffness of the reaction frame, two horizontal gantry frames are used. The model elements are placed inside the frames with a certain type of hinge in between to ensure that no moment would occur during the test. Moreover, to avoid friction between the element and the reaction floor, several columns with spherical hinge bearing on its top are installed before the elements are placed.
4.2.1. General description Compression–bending testing combines the loading patterns of imposed axial load and bending moment. As immersed tunnel elements will be located at different water depths, the pressure acting on an immersion joint will vary with its location. During seismic movement of the stratum, the horizontal bending might change with the location along the tunnel length. Then a maximum bending moment can be obtained as the input maximum moment in the test. Hence, the loading is set at 5 stages with different axial forces but the same bending moment, as displayed in Fig. 10. It should be note that the loading rate in the test is about 1 kN/s. The axial loading levels applied to the joint, listed in Table 2, account for the typical water pressure such as minimum water pressure and maximum water pressure. The bending moment, with a maximum value of 350 kN m, is applied to the joint when the axial force reaches a given level. The process for applying the bending moment is as follows (Fig. 11): After the initial unloaded situation, the axial force is increased to each of the predefined levels given in Table 2 (Fig. 11(b)). Then by adjusting the force of the jacks, a bending moment is applied to the joint (Fig. 11(c)). 4.2.2. Axial load application Compression loading is enforced through 4 hydraulic jacks. Their forces are increased synchronously until the total axial force reaches a target load level, as specified in Table 2. After the cyclic bending in the final stage, the jacks are gradually unloaded till the axial force becomes zero. The compression of the joint is measured at each loading/unloading stage, to get the relation between axial force and the compression of the joint. 4.2.3. Cyclic bending application Cyclic bending can be produced by differentiating the forces of the hydraulic jacks. At each loading stage, keep one couple of jacks (i.e. L1/L4) continue to load, while the other couple of jacks (correspondingly L2/L3) starts to unload. A bending moment will result in the joint. When the maximum value (350 kN m) in the joint is reached, the two couples of jacks start to work inversely to produce a ‘negative’ moment in the joint till the maximum value is reached. Then, all the jacks are operated to their original equal forces, which makes the bending moment to return to zero. In this way a bending moment loading cycle is completed. The compression of the joint is measured continuously during a loading/unloading cycle, in order to obtain the rotation of the joint as a function of the bending moment. 5. Axial performance of immersion joint 5.1. Compression–release curve Recorded data of compression and release with axial force is plotted in Fig. 12. It shows the compression (closing) of the joint reaches a maximum value of 13.6 mm when it is subjected to an axial force of 2500 kN. Then, compression recovers (extension of the joint) with decrease of the axial force. Finally, when the axial
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(a) Detailed view of immersion joint (GINA seal)
(b) Full view of the model before the test Fig. 7. Detailed and full views of the model.
load is 0, a residual compression of 3.1 mm remains, which is about 22.7% of the maximum compression. The occurrence of residual compression and a hysteretic loop between loading and unloading imply that the material of the GINA-type seal behaves viscoelastic, rather than hyper-elastic. Obviously, the compression–release curve can be divided into four portions. At initial loading, the slope of the curve of portion OA is about constant up to an axial force of 320 kN. At portion AB of the curve, the slope is no longer constant. The rapid change of it shows the same trend as in Fig. 6. This means that the axial stiffness of the immersion joint is increasing with the axial force, and the amount of compression of the joint reaches almost its limit at the final load level of 2500 kN. The slope of the curve at initial unloading, portion BC, drops steeply. Release of the compression mainly happens in portion CD when the axial force is less than 500 kN. The slope of this portion is nearly the same as that of the initial loading portion OA. The values of dA to dD are 6.29 mm, 13.60 mm, 11.54 mm and 3.11 mm respectively. In Fig. 12, two horizontal dotted lines are indicated, corresponding to the maximum water depth (MaWD) and minimum water depth (MiWD), with values equal to 1760 kN and 440 kN respectively. Obviously, both portions OA and CD are beneath the line of the MiWD. About the upper third of portion AB and portion BC
are above the line of the MaWD, the rest of which is in the range between MaWD and MiWD. Hence, the immersion joints close to the MiWD behave less stiff, resulting in larger deformations. On the contrary, smaller deformations occur in the immersion joints which are situated in deeper sea. Moreover, below the line of the MiWD, the compression is much more sensitive to the axial force. A slight drop of the axial force will cause large deformation in the joint, resulting in extension of the joint. Hence, the softer GINAtype seal can be used here to ensure that the compression will be kept larger than the minimum compression. With respect to the joints close to the line of MaWD, stiffer GINA-type seal can be used to avoid excessive compression. 5.2. Axial stiffness of the joint In order to quantify the relationship between the axial force and the compression of immersion joint, fitting curves F1 to F4 for each portion were determined to describe the compression–force relation of the model joint, which are presented in Fig. 13. The coefficients of the fitting curves are listed in Table 3. The coefficients of determination in Table 3 are used to measure the goodness of fit. It can be seen that at the level of low axial force, F1 and F4 nearly share the same slope, between which the difference is only about
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1500 1200
3000
1200
2760
Reaction Wall
Horizontal Reaction Frame
Hinges
Model Element B
Joint
Model Element A
Hinges
674
Supporting Columns
(a) Layout of test set-up (Plane View)
Loading Point
Loading Point
Supporting Columns with Spherical Top Reaction Floor
(b) A-A view of test set-up Fig. 8. Loading test set-up.
Fig. 9. Measurement lay-out.
7%. A difference is found between the peaks of the fitted loading and unloading curve. The application conditions of the fitted curves vary from the loading situation. It is also noted that, with respect to the loading portion, the fitting curve is continuously differentiable at point A, so as to point C in the unloading part. Hence, once the axial force is determined, the corresponding static axial stiffness can be calculated. For different construction water depths and loading situations, the initial water pressure is different and so is the axial spring stiffness k0 . The equation for the stiffness k0 is obtained as the first derivative of F, which is also the slope of the tangent line at the point.
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observed as well. After a complete loading cycle, the final residual rotation of the joint reaches 3.45 103 rad. The curve in Fig. 14 can be divided into 6 portions. At the beginning of the curve, the slope of portion O0 A0 is constant up to a rotation of 2.88 104 rad. At the transition point A0 , the slope of the next portion A0 B0 changes slightly but it is still another constant with rotation till 8.27 104 rad. After reaching the peak B0 , the curve enters the unloading part. During this part, portion B0 C 0 , the slope first drops remarkably then gradually tends to be some constant, which is close to that of portion O0 A0 , resulting in a residual rotation C 0 . The reverse loading potion C 0 D0 follows portion B0 C 0 . At the initial reverse loading part, the rotation still remain positive and the slope of this part is a constant till the rotation of 3.66 104 rad at point D0 . Like the slope of portion A0 B0 , that
Fig. 10. Quasi-static loading patterns.
of portion D0 E0 is also a constant, which is slightly smaller than that
8 k1 > > > < k2 dF ¼ k0 ðkN=mmÞ ¼ > k3 dd > > : k4
¼ 50:895
0 < d 6 dA
¼ 67:370d 372:699
dA < d 6 dB
¼ 940:848d 10805:235 dB < d 6 dC ¼ 47:450
dC < d 6 dD ð1Þ
where F and d are the compression force and compression respectively. k1 to k4 correspond to the portions OA to CD. dA to dD are the compressions at point A to D. The axial stiffness for both loading and unloading is described by a bi-linear model. The calculated axial stiffness for some particular axial forces is listed in Table 4. Obviously, in the portion AB and BC, the unloading axial stiffness is about two to three times the loading axial stiffness, showing the hysteresis behaviors of the GINA-type seal subjected to axial loading. When the axial force remains at a sufficiently low level, the values of both loading and unloading stiffness are almost equal. By using Eq. (1), the loading and unloading axial stiffness of the immersion joint in different water depths can be predicted.
6. Flexural performance of immersion joint
To characterize the flexural performance of the immersion joint, the moment–rotation curve for an axial force of 500 kN is presented in Fig. 14. In the beginning of the test, the rotation increases nearly linearly with the moment. Then the slope of the curve experiences a slight downward trend. The peak rotation of the immersion joint is 8.27 104 rad. Along the unloading part, there is a continuous decrease of the slope of the curve. Like in Fig. 12, also a residual rotation occurs in this case. When the moment increases reversely, the same increasing trend of the rotation can be
Table 2 Loading stages. Total axial force (kN)
1
500
2
1000
3 4
1500 2000
5
2500
can be found in portion E0 F 0 , compared to portion B0 C 0 . After applying a cyclic bending moment, there is a residual rotation occurring, resulting in an asymmetric deformation of the immersion joint. 6.2. Relative displacement of the joint Differential displacement of the joint would result from its unbalanced loading/unloading, when subjected to bending moment. It can be calculated from the measured displacements at each logged point, with respect to its initial compressive state. Fig. 15 illustrates the relative displacement of the joint under the axial force of 500 kN when subjected to a bending moment of 350 kN m. The initial state refers to the current compression of the joint while no bending moment has been applied. That is, no relative displacement occurs in the initial state for no moment is applied. In this situation, it is obvious that the relative displacement increases with the moment. In portion OA0 B0 , the displacement of the joint behaves symmetrically, as shown in Fig. 15(a), and the symmetry axis of the joint nearly remains in its geometric center during the cyclic bending. After unloading, the deformation of the joint cannot return to the initial state, which is shown in Fig. 15(b). Regarding to reverse loading part C 0 D0 E0 , thought the ini-
6.1. Moment–rotation curve
Stages
of portion C 0 D0 . Then the reverse loading curve peaks at point E0 . Subsequently, the reverse unloading starts and the same trend
Bending moments (kN m)
Remark
350
Minimum water pressure (440 kN) Final immersion joint (850 kN) – Maximum water pressure (1760 kN) –
tial state is different from portion OA0 B0 , the joint nearly behaves symmetrically and the maximum relative displacements are almost the same as the loading ones. During the loading and reverse loading process, it can be observed that the joint remains plane during compressive bending. 6.3. Rotation of the joint Table 5 lists the rotation of the joint under different levels of compressive bending. During the test, 5 levels of axial force and 4 levels of bending moment are considered. It is clear that for the same magnitude of bending moment, the rotations of the joint decrease as the axial force increases. The rotation corresponding to the axial force of 500 kN is about 10 times larger than that at 2500 kN. From another view, with respect to the same magnitude of axial force, the rotations increase along with the bending moments. Also, rotations change non-linearly along with both axial force and bending moment. Fig. 16 provides the moment–rotation curves of the immersion joint at different axial forces. The same trend as that in Fig. 14 can be observed. It is obvious that all the curves present the hysteretic behavior of the joint.
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Fig. 11. Loading process of immersion joint.
u
Fig. 12. Force–compression curve of immersion joint in the test.
Comparing the different curves in Fig. 16, the envelop area decreases along with the increasing axial force. That is, when the axial force grows gradually, the compressive stiffness of GINAtype rubber increases rapidly. Also, the slope of the curves changes continuously during the test and a residual deformation occurs after each case. 6.4. Flexural stiffness of the joint Two types of stiffness of the tested immersion joint are defined in Fig. 17, which are the secant loading stiffness ks and the secant
unloading stiffness ks respectively. The definition of the initial stiffness is the same as the aforementioned stiffness k0 .For the loading branch, the secant flexural stiffness of the immersion joint are presented in Fig. 18, which shows an increasing trend with the applied axial force. Polynomial fitting curves were developed. This flexural stiffness increases significantly, i.e. by one order of magnitude and hence, the variation of flexural stiffness needs to be considered in design. It follows that the behavior of the immersion joint varies according to the real loading situation and it will be difficult to evaluate the performance of the immersion joint during earthquake. For the unloading branch, the unloading secant stiffness is also shown in Fig. 18. Obviously, the flexural unloading stiffnesses increase with the axial force. From the slope of the curve, it can be found that, at the beginning of the curve, the flexural stiffness remains a high level, much larger than that of ks . Then with the decrease of the axial force, the flexural unloading stiffness experiences a downwards trend and soon drops by 2 orders of magnitude. At the level of axial force of 500 kN, the unloading flexural stiffness is close to the loading flexural stiffness. It is clear that the changing trend of flexural stiffness follows that of the axial force. At each level of axial force, the situation of the GINA-type seal is different. Once the GINA-type seal is highly compressed, the corresponding rotation of the joint subjected to moment changes little, which results in the occurrence of a larger loading flexural stiffness as well as an unloading one. On the contrary, when the axial force is 500 kN, the loading flexural stiffness has the same magnitude as that of the unloading one, which means that the GINA-type seal in the joint behaves elastically and the residual deformation is small. Also, the non-linear performance of the stiffness of the joint along with the axial force is obtained. The polynomial fitting curves and corresponding equations for flexural stiffness are given in Fig. 18. The values of flexural stiffness are listed in Table 6. The loading and unloading flexural stiffness of the joint subjected to a certain axial force can be predicted by using the presented equations.
Table 3 Coefficient of fitting function.
Fig. 13. Test results and the corresponding fitting curves.
Quadratic fitting function: F = ad2 + bd + c
Coefficient of determination
Portion
a
b
c
R-square
OA
0
50.895
0
–
AB
33.685
372.699
1331.656
0.9954
BC
470.424
10805.235
62445.527
0.6718
CD
0
47.450
147.331
–
Units: F (kN), d (mm)
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W. Xiao et al. / Tunnelling and Underground Space Technology 49 (2015) 426–437 Table 4 Axial spring stiffness for different water pressures (Scale 1:10). Axial force (kN)
Compression (mm) Loading
Unloading
200 440 850 1000 1500 1760 2000 2500
4.84 7.16 9.44 10.03 11.55 12.17 12.66 13.59
7.32 11.78 12.46 12.62 13.01 13.19 13.32 13.59
Initial loading axial stiffness (kN/mm)
Unloading axial stiffness (kN/mm)
50.90 109.67 263.27 303.02 405.42 447.19 480.21 542.86
47.45 278.55 921.46 1063.64 1439.51 1600.45 1735.81 1988.44
7. Stiffness ratio of the joint
(a) Loading poron of moment-rotaon curve
Another concern for immersed tunnel design is the ratio of the stiffness of the joint to that of the tunnel structure. An index for the ratio of stiffness is defined: j
r axial ¼
kaxial s kaxial
r bend ¼
kbend s kbend
ð2Þ
j
j
ð3Þ s
where kaxial and kaxial are the axial stiffness of the immersion joint j
and the tunnel structure (per unit length) respectively; kbend and s kbend are the flexural stiffness of the immersion joint and the tunnel j
j
structure (per unit length) respectively. kaxial and kbend are obtained by the method described in Fig. 17 from the large scale model test s s while kaxial and kbend are constants, which are determined by the Young’s modulus of concrete and the properties of the crosssection of the tunnel (per unit length). Based on these definitions, r axial and rbend are calculated and displayed in Figs. 19 and 20. Fig. 19 shows the axial ratio r axial of the tested immersion joint. During the test, the GINA-type seal in the joint is compressed continuously and becomes stiffer as the axial force increases. At the beginning of the test, the axial stiffness of the tunnel structure is about 1/1200 as that of the immersion joint. Then the ratio soon increases up to around 1/200 for an axial force of 1000 kN. At this stage, large displacements occur in the immersion joint, as shown in Fig. 12, and the deformation of the concrete can be ignored. Then
Fig. 14. Moment–rotation curve of immersion joint in the test (with axial force of 500 kN).
(b) Reverse loading poron of moment-rotaon curve Fig. 15. Rotation of immersion joint in the test (with axial force of 500 kN).
Table 5 Rotation of the joint under compressive bending (rad). Axial force (kN)
500 1000 1500 2000 2500
Bending moment (kN m) 84
168
252
350
1.34 104 4.89 105 3.07 105 1.82 105 1.17 105
2.88 104 8.91 105 6.28 105 4.38 105 2.99 105
5.07 104 1.58 104 1.09 104 6.64 105 5.04 105
8.27 104 2.47 104 1.55 104 9.56 105 6.64 105
a stage with continuous growth follows as the axial force increases from 1000 kN to 2000 kN. After that, the ratio remains around 1/100. The compression during this stage changes little, which can be seen in Fig. 12. The axial stiffness ratio in service condition is ranging between 1/362 and 1/118, depending on the water depth. The secant loading flexural stiffness ratios are presented in Fig. 20. The flexural stiffness ratio experiences the same increasing trend as that in Fig. 19. The peak ratio at different levels of axial force all appears in the situation of maximum axial force, among which the maximum value is 1/15.6. This flexural ratio behaves similarly as the axial force increases because in this situation the GINA-type seal is highly compressed and its stiffness varies little. The flexural loading stiffness ratio in service condition ranges from 1/29 to 1/212. Given the practical calculations, the axial and flexural stiffness ratios of immersion joint can be predicted for different water depths, which could be useful for simulation.
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Fig. 16. Moment–rotation curves of immersion joint in the test.
Fig. 19. Axial ratio of the tested immersion joint.
Table 6 Flexural stiffness of immersion joint subjected to axial force (MN m/rad). F (kN)
500
1000
1500
2000
2500
ks u ks
423 762
1414 4359
2262 15,983
3660 29,969
5269 31,967
Fig. 20. Flexural ratio of the tested immersion joint.
8. Conclusions
Fig. 17. Definition of stiffness of immersion joint.
Fig. 18. Flexural loading stiffness of immersion joint in the test.
This study presents the test of a scaled immersion joint subjected to compressive–bending. According to a practical project of Hong Kong-Zhuhai-Macau Link, compressive loads along the longitudinal direction of the immersed tunnel are applied in several levels, and equal amplitude of horizontal bending moment is applied at target axial forces. Analysis of the experimental results gives the following conclusion: (1) The axial stiffness of the immersion joint varies with levels of axial force, whether loading or unloading. In service condition, the stiffness of the joint falls in relative linear state with values ranging from 1/360 to 1/120 that of element. (2) The hysteretic loop of compression–force curve indicates that recovery of compression during unloading does follow the same path as for loading. Residual compression of joint warns that removal of the axial force is unsafe to the water tightness of the joint. (3) The joint remains plane during bending. Rotation of the joint increases with bending moment but it decreases with axial force. (4) The moment–rotation curve shows a hysteretic loop. It indicates that there is energy–dissipation during bending. However, the area of the loop reduces with increasing of
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axial force. The deformation of the joint might be asymmetric as the residual rotation of it is observed at each bending cycle. (5) Flexural stiffness of the joint increases with axial forces during bending. The joint works in nonlinear state at service condition. Its flexural stiffness varies from low boundary 1/ 212 to up boundary 1/29 of that of the element. It should be noted, however, that the conclusions are drawn according to scaled tests. Size effect should be taken into consideration in practical usage. Acknowledgements The research has been supported by the National Natural Science Foundation of China (51208296 & 51478343) and the Shanghai Committee of Science and Technology (13231200503). The authors acknowledge the support from the Fundamental Research Funds for the Central Universities (2013KJ095 & 101201438), Shanghai Educational Development Foundation (13CG17), and the National Key Technology R&D Program (2011BAG07B01 & 2012BAK24B04). References Akimoto, K., Hashidate, Y., Kitayama, H., Kumagai, K., 2002. Immersed tunnels in Japan: recent technological trends. Underwater Technology. In: Proceedings of the 2002 International Symposium on, 2002, pp. 81–86, http://dx.doi.org/10. 1109/UT.2002.1002393.
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Anastasopoulos, I., Gerolymos, N., Drosos, V., Kourkoulis, R., Georgarakos, T., Gazetas, G., 2007. Nonlinear response of deep immersed tunnel to strong seismic shaking. J. Geotechn. Geoenviron. Eng. 133 (9), 1067–1090. http://dx. doi.org/10.1061/(ASCE)1090-0241(2007) 133:9(1067). CCCCHZMB, 2011. Tunnel Design Solution [Format: Images].. Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2010. Code for Design of Concrete Structure (GB 50010-2010). China Architecture & Building Press, Beijing. Hamazaki, Y., Yamaguchi, K., Tekehana, N., Nagata, K., Fukumoto, K., Nanjo, T., et al., 1999. 沈埋トンネル用の鋼製柔継手 (Steel spring joint for immersed tunnel). R&D (神戸製鋼技報) 2 (49), 57–60, . Ingerslev, C., 2010. Immersed and floating tunnels. Procedia Eng. 4, 51–59. http:// dx.doi.org/10.1016/j.proeng.2010.08.007. ITA Working Group 11, 2011. Immersed and Floating Tunnels (Report No. 007/ OCT2011). International Tunneling and Underground Space Association (ITA), Lausanne. Kiyomiya, O., Fujisawa, T., Yamada, M., Honda, M., 1992. 沈埋トンネル柔継手の力学 性状 (Mechanical Properties of Flexible Joint between Submerged Tunnel Elements (Report No. 728)). Port and Harbour Research Institute, Yokosuka, Japan. Kiyomiya, O., Nakamichi, M., Yokota, H., Shiraishi, S., 2004. New type flexible joint for the Osaka Port Yumeshima Tunnel. In: Proceedings of OCEANS ’04. MTTS/ IEEE TECHNO-OCEAN ’04, 4, pp. 2086–2091, http://dx.doi.org/10.1109/OCEANS. 2004.1406465. Liu, Z., 2009. Behaviour and Security Assessment of Joints of Immersed Tunnel (Master’s thesis). Tongji University, Shanghai. Owen, N., Scholl, R., 1981. Earthquake Engineering of Large Underground Structures. URS/John A. Blume & Associates, Engineers, San Francisco, California. Van Oorsouw, R.S., 2010. Behavior of Segment Joints in Immersed Tunnels under Seismic Loading (Master’s thesis). Delft University of Technology. Delft. Yu, H., Yuan, Y., Liu, H., Li, Z., 2014. Mechanical model and analytical solution of stiffness for joints of immersed-tube tunnel. Eng. Mech. 31 (6), 145–150. http:// dx.doi.org/10.6052/j.issn.1000-4750.2012.012.0987.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Compression–bending behavior of a scaled immersion joint Wenhao Xiao a, Haitao Yu b, Yong Yuan c,⇑, Luc Taerwe a,d, Rui Chai e a
Department of Structural Engineering, Ghent University, Ghent, Belgium Key Laboratory of Geotechnical and Underground Engineering (Tongji University) of Ministry of Education, Tongji University, Shanghai 200092, China c State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China d High-End Foreign Expert at Tongji University, Shanghai, China e Hong Kong-Zhuhai-Macao Bridge Authority, Zhuhai 519095, China b
a r t i c l e
i n f o
Article history: Received 8 August 2014 Received in revised form 23 May 2015 Accepted 2 June 2015 Available online 17 June 2015 Keywords: Immersed tunnel Element joint Compressive–bending test Scaled model Stiffness
a b s t r a c t The mechanical behavior of an element joint of an immersed tunnel subjected to quasi-static axial compression and horizontal bending is investigated in this research. To explore the performance of the immersion joint compression–bending loads are applied on a scaled specimen in specific patterns, which are designed based on a practical project. It is found that the extension and closure of the immersion joint vary non-linearly with applied axial forces. Fitting equations for axial stiffness are correspondingly given with regard to loading and unloading states of the joint. Under bending action the element edges which constitute the immersion joint still remain plane. Observed rotations of the joint are non-linearly increasing with bending moment, whether it is pushed forward or bend inversely. Hysteresis behavior obviously exists and the hysteretic loop tends to contract with the increase of the axial force. The stiffness ratio of the joint with respect to that of the tunnel element in service states ranges from 1/360 to 1/120 for the axial stiffness, and from 1/29 to 1/212 for the flexural stiffness. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction An immersed tunnel consists of precast tunnel elements. The tunnel elements are being floated to the construction site and then are immersed in a trench excavated in the bottom of a water way. The immersion joints, which are connecting adjacent elements, are the weakest units in the whole tunnel (Ingerslev, 2010; ITA Working Group 11, 2011). According to the stiffness ratio of the joint to the element, immersion joints can be divided into three categories: rigid joints, flexible joints and partial-rigid (or partialflexible) joints. Akimoto et al. (2002) summarized the types of immersion joint developed in Japan. Whatever the type of immersion joint is, the design of it has to consider various actions during its service life, water pressure, earthquake, settlement of foundation, shock from shipwrecks, and other actions. Meanwhile, an immersion joint should include the water-proof part as an indispensable system. Therefore, knowledge of the deformation of a joint under loading is important for a safe, reliable, and water-proof design. Further, due to the water pressure in the construction phase, the immersion joint is submitted to an initial compression. It is vital to know the behavior of the ⇑ Corresponding author at: R326 Geotechnical Building, Tongji University, 1239 Siping Road, Shanghai 200092, China. E-mail address: [email protected] (Y. Yuan). http://dx.doi.org/10.1016/j.tust.2015.06.002 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
immersion joint after immersion. Therefore, the axial stiffness for this situation is required for calculation and design. Theoretically, the mechanical behavior of an immersion joint was considered under imposed deformation (Liu, 2009) or under seismic action (Anastasopoulos et al., 2007). Yu et al. (2014) deduced a bi-linear formula to account for the stiffness of a flexible joint, which was also verified through numerical modeling. It should be noted that there are not much experimental works reported on immersion joints even though they came to practical applications for more than 100 years. Kiyomiya et al. (1992) performed a quasi-static test for the mechanical properties of a flexible joint with 1/4 geometric scale. In this test the flexural and compression behaviors of a joint were obtained. The results showed that the immersion joint behaved non-linearly in quasistatic and quasi-dynamic cases. Kiyomiya et al. (2004) also carried out both a 3-dimensional experiment and a finite element analysis for a new type of flexible joint referred to as the Crown Seal. Results of both tests indicated that this new type of joint can be applied in practice because of the effective reduction of deformation with this particular design. Hamazaki et al. (1999) applied a new type of steel device to the immersion joint. In these experiments, the axial and transversal mechanical properties of the joint were studied under static, cyclic and eccentric loading. The results showed that this device can play a role in energy dissipation. It can be seen that the behavior of immersion joints was often simplified
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as a bi-linear curve or the stiffness was regarded as a constant, which cannot reflect the real behavior of an immersion joint. However, former researchers mostly dealt with the response of a complete tunnel. Results in the tests done by Kiyomiya et al. (1992) also proved this. Moreover, only a few experiments were found about the flexural mechanical behavior of large-scale immersion joints as well as its flexural stiffness. It should be noted that extension of the immersion joint may be caused from compression and tension due to different types of actions in tunnel elements. The differential extension of the immersion joint may be introduced as ‘‘snake” movement of an immersed tunnel along its longitudinal profile, whether from settlement of foundation or from stratum movement during earthquake (Owen and Scholl, 1981). This paper presents a compression–bending static test of a halfflexible immersion joint with a 1:10 geometric scale. Modeling techniques for the scaled immersion joint were applied. For the experiment on the mechanical behavior of the immersion joint, considering the system model, measurement system and loading patterns, were defined. The compression on the scaled model is applied axially to simulate the water pressure on the immersion joint at typical buried depths. Bending moments are applied cyclically at equal amplitude in the horizontal plane, by varying the load in the axial hydraulic jacks on each sidewall of the element. Through observed load–deformation curves, both the axial stiffness and the flexural stiffness of the joint will be derived for use in practice.
427
segmental joints. The cross-sectional dimension of the immersion joint is about 37.95 m 11.40 m (Fig. 2(a)). The partial-flexible immersion joint generally includes a GINA seal, an Omega water proof, shear keys and steel shell shown in Fig. 2. When the immersed tunnel is installed, the GINA seal between elements will be pressed tightly with a minimum compression, resulting in a waterproof sealing due to initial water pressure. The initial water pressure varies from the depth of the immersion joint, resulting in different initial axial force in the joints. Therefore, the purpose of the GINA seal is to seal the immersion joints between two adjacent tunnel elements, ensuring the water tightness of the structure. If the GINA seal fails, the Omega water proof, as the second water tightness defense, will start to work to avoid severe leakage. As a result of earthquake loading and differential settlement, ground motion will cause movement of the immersed tunnel. This movement will result in an extra axial force and a transversal force on the immersion joints (Van Oorsouw, 2010). The force in axial direction works on the cross section of the joint as well as the moment and they will be transferred from one element to another through the GINA seal. Moreover, shear keys are used to transfer transversal forces. Hence, to study the flexural mechanical behavior of the immersion joint, only the GINA seal component is considered in this paper. 2.2. Deformation of immersion joint
2. Background 2.1. Immersion joints As mentioned above, the immersion joints differ in stiffness and in this paper, the half-flexible one is presented. This choice is based on the real project of the Hong Kong–Zhuhai–Macao link which is under construction. The immersed tunnel in this project is approximately 5664 m in length. It consists of 33 elements and is finally connected to two artificial islands, as can be seen in Fig. 1. The length of a typical element is 180 m and is assembled through 8 segments with 22.5 m in length between which are
From the researches by Owen and Scholl (1981), the deformation mode of underground structures subjected to earthquake loading can be divided into three categories: compression/extension, bending and racking. Regarding immersed tunnels, the first two modes dominate the deformation of immersion joint during earthquake. In this study, the effect of longitudinal bending is mainly considered to express flexural mechanical behavior of immersion joints. As can be seen in Fig. 3, when the joint is subjected to axial force, the axial compression d occurs in the joint. If the axial force and bending moment are applied together, the joint is compressed and rotates which means that both compression d and rotation h
Fig. 1. Sketch of immersed tunnel in HZMB (CCCCHZMB, 2011).
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(a) Original profile of immersion joint
(b) Detail view of A-A Fig. 2. Immersion joint in HZMB.
Fig. 3. Compression and bending of immersion joint.
occur. Hence, various loading cases can be considered to analyze this bending deformation by controlling the axial force and bending moment.
3. Scaled model of immersion joint 3.1. Model element of the tunnel The original profile of cross-section of a tunnel element, which was adopted in HZMB, is shown in Fig. 2(a). It consists of two vehicle passages and one gallery serving for emergency. Bending of the immersion joint could happen either in the vertical or horizontal plane. For the consideration of loading, here only horizontal bending will be applied. As the shaped corners in passages and middle walls contribute insignificantly to compression or bending of the joint, the cross-sectional profile of the model element was simplified as rectangular and the middle walls were not considered as Fig. 4(b) and (c) display, compared to the original cross-section.
Furthermore, the shaded parts refer to the horizontal steel shear keys. Based on the capacity of available testing facilities and the goal of the experiment, a geometric scale of 1:10 is selected. The geometric reinforcement ratio for model is the same as that in HZMB. But in the vicinity of the joint, the model element was enhanced. Fig. 4 also provides the dimensions of a single tunnel element with a width of 3800 mm, a height of 1150 mm, and a length of 1250 mm, as well as a 150 mm-thick concrete slab. Referring to the Chinese Code for concrete structure (GB500102010), the types of concrete and reinforcement are C50 and HRB335 respectively. 3.2. Model immersion joint The model immersion joint follows the design of HZMB and the lay-out is also simplified according to the experiment. The steel shell and omega profile are not adopted in this model joint due to the lack of contribution to flexural behavior of the immersion joint.
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(a) Model tunnel
(b) Model Element A
(c) Model Element B
Fig. 4. Cross-section of model immersed tunnel (units: mm).
3.2.1. Steel shear keys In the real immersion joint, shear keys will be situated in walls and slabs as shown in Fig. 2(a). As horizontal seismic loading is considered in this test, vertical shear keys are not provided and also the inner walls have been deleted. However, the horizontal shear keys are design based on the HZMB project with geometric scale of 1:10. With respect to the flexural behavior of the immersion joint in this test, shear keys will not be active during the test. Hence, the behavior of the steel shear keys is not discussed in this paper. 3.2.2. GINA-type seal A certain type of GINA seal is designed and manufactured independently for this experiment. Fig. 5 displays the dimensions of the model GINA profile, and Table 1 lists its physical parameters. Fig. 6 shows the load–compression curves of GINA-type, which is obtained in material test. The loading rate is the same as that in the following test. From the graph it can be seen that the GINA-type seal becomes stiffer when the compression force increases. The variation in slope
(a) Dimension of the model GINA-type (unit:mm)
Table 1 Physical characteristics of the rubber used for the GINA-type seal (provided by producers). Characteristic
Value
Hardness Breaking tenacity Extensibility Allowable compressive strength Shear modulus Friction coefficient
55–60 Shore A 14 MPa >450% 10 MPa 0.98–1.47 MPa Steel:0.2; Concrete:0.3
can partly be attributed to the specific geometry of the GINA-type seal (see Fig. 5) for which the total height of the smaller top part is about 8.5 mm. It also can be seen in Fig. 6 that the behavior of the Trelleborg GINA as used in the HZMB project and the model GINA-type are close to each other. Under the maximum applied load of 2500 kN, the maximum compression of the Trelleborg GINA and the model GINA-type is 19.0 mm and 20.4 mm respectively, with
(b) GINA-type profile
Fig. 5. Dimensions of the model GINA-type profile.
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4.1.3. Measurement lay-out and data acquisition system During the test, in order to figure out the flexural behavior of the immersion joint, the deformation of the joint needs to be monitored. Hence, 5 displacement transducers are placed to accomplish it, which are shown in Fig. 9. The transducers are situated evenly along the joint in order to obtain the distribution of the displacement along the joint as well as its rotation. These displacements are collected by a digital data acquisition system. 4.2. Loading protocol
Fig. 6. Comparison of load–compression curves of Trelleborg GINA and model GINA-type (loading rate: 1 kN/s).
only 7% difference between them. After installation, the detailed and full views of model are shown in Fig. 7.
4. Compression–bending test 4.1. Loading test set-up 4.1.1. Loading system As illustrated in Fig. 8, the tunnel model was placed in a steel loading frame. During a typical experiment, one tunnel element (Model Element A) is fixed horizontally while the other one (Model Element B) is movable, resulting in a deformation of the immersion joint. This test set-up, which is designed by our research group, mainly consists of an axial part and a transversal part in order to meet the demand of the experiment. This reaction frame can provide the following particular functions: (1) One model element inside the frame can have 2 degrees of freedom in the horizontal plane while the other one needs to be fixed in the loading direction. (2) The stiffness of the reaction frame should be much larger than that of the immersion joint. Fig. 8(a) also shows the 4 loading points of the test. In the aforementioned description, the axial forces are applied to Model Element B. Thus, 4 hydraulic jacks are situated between this element and the reaction wall, displayed in Fig. 8. These jacks can only provide pressure to the element but no tension. The axial loading is applied by 4 hydraulic jacks in the end of Model Element B (Fig. 8(b)). By controlling the jacks, different levels of axial forces and bending moment can be applied in the element, which is detailed in next section. In order to figure out the flexural behavior of the immersion joint, this experiment employs a moment reversed quasi-static loading pattern.
4.1.2. Installation of model immersion joint According to the aforementioned loading system, a reaction frame was designed, including axial reaction part and a supporting system. To increase the axial stiffness of the reaction frame, two horizontal gantry frames are used. The model elements are placed inside the frames with a certain type of hinge in between to ensure that no moment would occur during the test. Moreover, to avoid friction between the element and the reaction floor, several columns with spherical hinge bearing on its top are installed before the elements are placed.
4.2.1. General description Compression–bending testing combines the loading patterns of imposed axial load and bending moment. As immersed tunnel elements will be located at different water depths, the pressure acting on an immersion joint will vary with its location. During seismic movement of the stratum, the horizontal bending might change with the location along the tunnel length. Then a maximum bending moment can be obtained as the input maximum moment in the test. Hence, the loading is set at 5 stages with different axial forces but the same bending moment, as displayed in Fig. 10. It should be note that the loading rate in the test is about 1 kN/s. The axial loading levels applied to the joint, listed in Table 2, account for the typical water pressure such as minimum water pressure and maximum water pressure. The bending moment, with a maximum value of 350 kN m, is applied to the joint when the axial force reaches a given level. The process for applying the bending moment is as follows (Fig. 11): After the initial unloaded situation, the axial force is increased to each of the predefined levels given in Table 2 (Fig. 11(b)). Then by adjusting the force of the jacks, a bending moment is applied to the joint (Fig. 11(c)). 4.2.2. Axial load application Compression loading is enforced through 4 hydraulic jacks. Their forces are increased synchronously until the total axial force reaches a target load level, as specified in Table 2. After the cyclic bending in the final stage, the jacks are gradually unloaded till the axial force becomes zero. The compression of the joint is measured at each loading/unloading stage, to get the relation between axial force and the compression of the joint. 4.2.3. Cyclic bending application Cyclic bending can be produced by differentiating the forces of the hydraulic jacks. At each loading stage, keep one couple of jacks (i.e. L1/L4) continue to load, while the other couple of jacks (correspondingly L2/L3) starts to unload. A bending moment will result in the joint. When the maximum value (350 kN m) in the joint is reached, the two couples of jacks start to work inversely to produce a ‘negative’ moment in the joint till the maximum value is reached. Then, all the jacks are operated to their original equal forces, which makes the bending moment to return to zero. In this way a bending moment loading cycle is completed. The compression of the joint is measured continuously during a loading/unloading cycle, in order to obtain the rotation of the joint as a function of the bending moment. 5. Axial performance of immersion joint 5.1. Compression–release curve Recorded data of compression and release with axial force is plotted in Fig. 12. It shows the compression (closing) of the joint reaches a maximum value of 13.6 mm when it is subjected to an axial force of 2500 kN. Then, compression recovers (extension of the joint) with decrease of the axial force. Finally, when the axial
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(a) Detailed view of immersion joint (GINA seal)
(b) Full view of the model before the test Fig. 7. Detailed and full views of the model.
load is 0, a residual compression of 3.1 mm remains, which is about 22.7% of the maximum compression. The occurrence of residual compression and a hysteretic loop between loading and unloading imply that the material of the GINA-type seal behaves viscoelastic, rather than hyper-elastic. Obviously, the compression–release curve can be divided into four portions. At initial loading, the slope of the curve of portion OA is about constant up to an axial force of 320 kN. At portion AB of the curve, the slope is no longer constant. The rapid change of it shows the same trend as in Fig. 6. This means that the axial stiffness of the immersion joint is increasing with the axial force, and the amount of compression of the joint reaches almost its limit at the final load level of 2500 kN. The slope of the curve at initial unloading, portion BC, drops steeply. Release of the compression mainly happens in portion CD when the axial force is less than 500 kN. The slope of this portion is nearly the same as that of the initial loading portion OA. The values of dA to dD are 6.29 mm, 13.60 mm, 11.54 mm and 3.11 mm respectively. In Fig. 12, two horizontal dotted lines are indicated, corresponding to the maximum water depth (MaWD) and minimum water depth (MiWD), with values equal to 1760 kN and 440 kN respectively. Obviously, both portions OA and CD are beneath the line of the MiWD. About the upper third of portion AB and portion BC
are above the line of the MaWD, the rest of which is in the range between MaWD and MiWD. Hence, the immersion joints close to the MiWD behave less stiff, resulting in larger deformations. On the contrary, smaller deformations occur in the immersion joints which are situated in deeper sea. Moreover, below the line of the MiWD, the compression is much more sensitive to the axial force. A slight drop of the axial force will cause large deformation in the joint, resulting in extension of the joint. Hence, the softer GINAtype seal can be used here to ensure that the compression will be kept larger than the minimum compression. With respect to the joints close to the line of MaWD, stiffer GINA-type seal can be used to avoid excessive compression. 5.2. Axial stiffness of the joint In order to quantify the relationship between the axial force and the compression of immersion joint, fitting curves F1 to F4 for each portion were determined to describe the compression–force relation of the model joint, which are presented in Fig. 13. The coefficients of the fitting curves are listed in Table 3. The coefficients of determination in Table 3 are used to measure the goodness of fit. It can be seen that at the level of low axial force, F1 and F4 nearly share the same slope, between which the difference is only about
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1500 1200
3000
1200
2760
Reaction Wall
Horizontal Reaction Frame
Hinges
Model Element B
Joint
Model Element A
Hinges
674
Supporting Columns
(a) Layout of test set-up (Plane View)
Loading Point
Loading Point
Supporting Columns with Spherical Top Reaction Floor
(b) A-A view of test set-up Fig. 8. Loading test set-up.
Fig. 9. Measurement lay-out.
7%. A difference is found between the peaks of the fitted loading and unloading curve. The application conditions of the fitted curves vary from the loading situation. It is also noted that, with respect to the loading portion, the fitting curve is continuously differentiable at point A, so as to point C in the unloading part. Hence, once the axial force is determined, the corresponding static axial stiffness can be calculated. For different construction water depths and loading situations, the initial water pressure is different and so is the axial spring stiffness k0 . The equation for the stiffness k0 is obtained as the first derivative of F, which is also the slope of the tangent line at the point.
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observed as well. After a complete loading cycle, the final residual rotation of the joint reaches 3.45 103 rad. The curve in Fig. 14 can be divided into 6 portions. At the beginning of the curve, the slope of portion O0 A0 is constant up to a rotation of 2.88 104 rad. At the transition point A0 , the slope of the next portion A0 B0 changes slightly but it is still another constant with rotation till 8.27 104 rad. After reaching the peak B0 , the curve enters the unloading part. During this part, portion B0 C 0 , the slope first drops remarkably then gradually tends to be some constant, which is close to that of portion O0 A0 , resulting in a residual rotation C 0 . The reverse loading potion C 0 D0 follows portion B0 C 0 . At the initial reverse loading part, the rotation still remain positive and the slope of this part is a constant till the rotation of 3.66 104 rad at point D0 . Like the slope of portion A0 B0 , that
Fig. 10. Quasi-static loading patterns.
of portion D0 E0 is also a constant, which is slightly smaller than that
8 k1 > > > < k2 dF ¼ k0 ðkN=mmÞ ¼ > k3 dd > > : k4
¼ 50:895
0 < d 6 dA
¼ 67:370d 372:699
dA < d 6 dB
¼ 940:848d 10805:235 dB < d 6 dC ¼ 47:450
dC < d 6 dD ð1Þ
where F and d are the compression force and compression respectively. k1 to k4 correspond to the portions OA to CD. dA to dD are the compressions at point A to D. The axial stiffness for both loading and unloading is described by a bi-linear model. The calculated axial stiffness for some particular axial forces is listed in Table 4. Obviously, in the portion AB and BC, the unloading axial stiffness is about two to three times the loading axial stiffness, showing the hysteresis behaviors of the GINA-type seal subjected to axial loading. When the axial force remains at a sufficiently low level, the values of both loading and unloading stiffness are almost equal. By using Eq. (1), the loading and unloading axial stiffness of the immersion joint in different water depths can be predicted.
6. Flexural performance of immersion joint
To characterize the flexural performance of the immersion joint, the moment–rotation curve for an axial force of 500 kN is presented in Fig. 14. In the beginning of the test, the rotation increases nearly linearly with the moment. Then the slope of the curve experiences a slight downward trend. The peak rotation of the immersion joint is 8.27 104 rad. Along the unloading part, there is a continuous decrease of the slope of the curve. Like in Fig. 12, also a residual rotation occurs in this case. When the moment increases reversely, the same increasing trend of the rotation can be
Table 2 Loading stages. Total axial force (kN)
1
500
2
1000
3 4
1500 2000
5
2500
can be found in portion E0 F 0 , compared to portion B0 C 0 . After applying a cyclic bending moment, there is a residual rotation occurring, resulting in an asymmetric deformation of the immersion joint. 6.2. Relative displacement of the joint Differential displacement of the joint would result from its unbalanced loading/unloading, when subjected to bending moment. It can be calculated from the measured displacements at each logged point, with respect to its initial compressive state. Fig. 15 illustrates the relative displacement of the joint under the axial force of 500 kN when subjected to a bending moment of 350 kN m. The initial state refers to the current compression of the joint while no bending moment has been applied. That is, no relative displacement occurs in the initial state for no moment is applied. In this situation, it is obvious that the relative displacement increases with the moment. In portion OA0 B0 , the displacement of the joint behaves symmetrically, as shown in Fig. 15(a), and the symmetry axis of the joint nearly remains in its geometric center during the cyclic bending. After unloading, the deformation of the joint cannot return to the initial state, which is shown in Fig. 15(b). Regarding to reverse loading part C 0 D0 E0 , thought the ini-
6.1. Moment–rotation curve
Stages
of portion C 0 D0 . Then the reverse loading curve peaks at point E0 . Subsequently, the reverse unloading starts and the same trend
Bending moments (kN m)
Remark
350
Minimum water pressure (440 kN) Final immersion joint (850 kN) – Maximum water pressure (1760 kN) –
tial state is different from portion OA0 B0 , the joint nearly behaves symmetrically and the maximum relative displacements are almost the same as the loading ones. During the loading and reverse loading process, it can be observed that the joint remains plane during compressive bending. 6.3. Rotation of the joint Table 5 lists the rotation of the joint under different levels of compressive bending. During the test, 5 levels of axial force and 4 levels of bending moment are considered. It is clear that for the same magnitude of bending moment, the rotations of the joint decrease as the axial force increases. The rotation corresponding to the axial force of 500 kN is about 10 times larger than that at 2500 kN. From another view, with respect to the same magnitude of axial force, the rotations increase along with the bending moments. Also, rotations change non-linearly along with both axial force and bending moment. Fig. 16 provides the moment–rotation curves of the immersion joint at different axial forces. The same trend as that in Fig. 14 can be observed. It is obvious that all the curves present the hysteretic behavior of the joint.
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Fig. 11. Loading process of immersion joint.
u
Fig. 12. Force–compression curve of immersion joint in the test.
Comparing the different curves in Fig. 16, the envelop area decreases along with the increasing axial force. That is, when the axial force grows gradually, the compressive stiffness of GINAtype rubber increases rapidly. Also, the slope of the curves changes continuously during the test and a residual deformation occurs after each case. 6.4. Flexural stiffness of the joint Two types of stiffness of the tested immersion joint are defined in Fig. 17, which are the secant loading stiffness ks and the secant
unloading stiffness ks respectively. The definition of the initial stiffness is the same as the aforementioned stiffness k0 .For the loading branch, the secant flexural stiffness of the immersion joint are presented in Fig. 18, which shows an increasing trend with the applied axial force. Polynomial fitting curves were developed. This flexural stiffness increases significantly, i.e. by one order of magnitude and hence, the variation of flexural stiffness needs to be considered in design. It follows that the behavior of the immersion joint varies according to the real loading situation and it will be difficult to evaluate the performance of the immersion joint during earthquake. For the unloading branch, the unloading secant stiffness is also shown in Fig. 18. Obviously, the flexural unloading stiffnesses increase with the axial force. From the slope of the curve, it can be found that, at the beginning of the curve, the flexural stiffness remains a high level, much larger than that of ks . Then with the decrease of the axial force, the flexural unloading stiffness experiences a downwards trend and soon drops by 2 orders of magnitude. At the level of axial force of 500 kN, the unloading flexural stiffness is close to the loading flexural stiffness. It is clear that the changing trend of flexural stiffness follows that of the axial force. At each level of axial force, the situation of the GINA-type seal is different. Once the GINA-type seal is highly compressed, the corresponding rotation of the joint subjected to moment changes little, which results in the occurrence of a larger loading flexural stiffness as well as an unloading one. On the contrary, when the axial force is 500 kN, the loading flexural stiffness has the same magnitude as that of the unloading one, which means that the GINA-type seal in the joint behaves elastically and the residual deformation is small. Also, the non-linear performance of the stiffness of the joint along with the axial force is obtained. The polynomial fitting curves and corresponding equations for flexural stiffness are given in Fig. 18. The values of flexural stiffness are listed in Table 6. The loading and unloading flexural stiffness of the joint subjected to a certain axial force can be predicted by using the presented equations.
Table 3 Coefficient of fitting function.
Fig. 13. Test results and the corresponding fitting curves.
Quadratic fitting function: F = ad2 + bd + c
Coefficient of determination
Portion
a
b
c
R-square
OA
0
50.895
0
–
AB
33.685
372.699
1331.656
0.9954
BC
470.424
10805.235
62445.527
0.6718
CD
0
47.450
147.331
–
Units: F (kN), d (mm)
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W. Xiao et al. / Tunnelling and Underground Space Technology 49 (2015) 426–437 Table 4 Axial spring stiffness for different water pressures (Scale 1:10). Axial force (kN)
Compression (mm) Loading
Unloading
200 440 850 1000 1500 1760 2000 2500
4.84 7.16 9.44 10.03 11.55 12.17 12.66 13.59
7.32 11.78 12.46 12.62 13.01 13.19 13.32 13.59
Initial loading axial stiffness (kN/mm)
Unloading axial stiffness (kN/mm)
50.90 109.67 263.27 303.02 405.42 447.19 480.21 542.86
47.45 278.55 921.46 1063.64 1439.51 1600.45 1735.81 1988.44
7. Stiffness ratio of the joint
(a) Loading poron of moment-rotaon curve
Another concern for immersed tunnel design is the ratio of the stiffness of the joint to that of the tunnel structure. An index for the ratio of stiffness is defined: j
r axial ¼
kaxial s kaxial
r bend ¼
kbend s kbend
ð2Þ
j
j
ð3Þ s
where kaxial and kaxial are the axial stiffness of the immersion joint j
and the tunnel structure (per unit length) respectively; kbend and s kbend are the flexural stiffness of the immersion joint and the tunnel j
j
structure (per unit length) respectively. kaxial and kbend are obtained by the method described in Fig. 17 from the large scale model test s s while kaxial and kbend are constants, which are determined by the Young’s modulus of concrete and the properties of the crosssection of the tunnel (per unit length). Based on these definitions, r axial and rbend are calculated and displayed in Figs. 19 and 20. Fig. 19 shows the axial ratio r axial of the tested immersion joint. During the test, the GINA-type seal in the joint is compressed continuously and becomes stiffer as the axial force increases. At the beginning of the test, the axial stiffness of the tunnel structure is about 1/1200 as that of the immersion joint. Then the ratio soon increases up to around 1/200 for an axial force of 1000 kN. At this stage, large displacements occur in the immersion joint, as shown in Fig. 12, and the deformation of the concrete can be ignored. Then
Fig. 14. Moment–rotation curve of immersion joint in the test (with axial force of 500 kN).
(b) Reverse loading poron of moment-rotaon curve Fig. 15. Rotation of immersion joint in the test (with axial force of 500 kN).
Table 5 Rotation of the joint under compressive bending (rad). Axial force (kN)
500 1000 1500 2000 2500
Bending moment (kN m) 84
168
252
350
1.34 104 4.89 105 3.07 105 1.82 105 1.17 105
2.88 104 8.91 105 6.28 105 4.38 105 2.99 105
5.07 104 1.58 104 1.09 104 6.64 105 5.04 105
8.27 104 2.47 104 1.55 104 9.56 105 6.64 105
a stage with continuous growth follows as the axial force increases from 1000 kN to 2000 kN. After that, the ratio remains around 1/100. The compression during this stage changes little, which can be seen in Fig. 12. The axial stiffness ratio in service condition is ranging between 1/362 and 1/118, depending on the water depth. The secant loading flexural stiffness ratios are presented in Fig. 20. The flexural stiffness ratio experiences the same increasing trend as that in Fig. 19. The peak ratio at different levels of axial force all appears in the situation of maximum axial force, among which the maximum value is 1/15.6. This flexural ratio behaves similarly as the axial force increases because in this situation the GINA-type seal is highly compressed and its stiffness varies little. The flexural loading stiffness ratio in service condition ranges from 1/29 to 1/212. Given the practical calculations, the axial and flexural stiffness ratios of immersion joint can be predicted for different water depths, which could be useful for simulation.
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Fig. 16. Moment–rotation curves of immersion joint in the test.
Fig. 19. Axial ratio of the tested immersion joint.
Table 6 Flexural stiffness of immersion joint subjected to axial force (MN m/rad). F (kN)
500
1000
1500
2000
2500
ks u ks
423 762
1414 4359
2262 15,983
3660 29,969
5269 31,967
Fig. 20. Flexural ratio of the tested immersion joint.
8. Conclusions
Fig. 17. Definition of stiffness of immersion joint.
Fig. 18. Flexural loading stiffness of immersion joint in the test.
This study presents the test of a scaled immersion joint subjected to compressive–bending. According to a practical project of Hong Kong-Zhuhai-Macau Link, compressive loads along the longitudinal direction of the immersed tunnel are applied in several levels, and equal amplitude of horizontal bending moment is applied at target axial forces. Analysis of the experimental results gives the following conclusion: (1) The axial stiffness of the immersion joint varies with levels of axial force, whether loading or unloading. In service condition, the stiffness of the joint falls in relative linear state with values ranging from 1/360 to 1/120 that of element. (2) The hysteretic loop of compression–force curve indicates that recovery of compression during unloading does follow the same path as for loading. Residual compression of joint warns that removal of the axial force is unsafe to the water tightness of the joint. (3) The joint remains plane during bending. Rotation of the joint increases with bending moment but it decreases with axial force. (4) The moment–rotation curve shows a hysteretic loop. It indicates that there is energy–dissipation during bending. However, the area of the loop reduces with increasing of
W. Xiao et al. / Tunnelling and Underground Space Technology 49 (2015) 426–437
axial force. The deformation of the joint might be asymmetric as the residual rotation of it is observed at each bending cycle. (5) Flexural stiffness of the joint increases with axial forces during bending. The joint works in nonlinear state at service condition. Its flexural stiffness varies from low boundary 1/ 212 to up boundary 1/29 of that of the element. It should be noted, however, that the conclusions are drawn according to scaled tests. Size effect should be taken into consideration in practical usage. Acknowledgements The research has been supported by the National Natural Science Foundation of China (51208296 & 51478343) and the Shanghai Committee of Science and Technology (13231200503). The authors acknowledge the support from the Fundamental Research Funds for the Central Universities (2013KJ095 & 101201438), Shanghai Educational Development Foundation (13CG17), and the National Key Technology R&D Program (2011BAG07B01 & 2012BAK24B04). References Akimoto, K., Hashidate, Y., Kitayama, H., Kumagai, K., 2002. Immersed tunnels in Japan: recent technological trends. Underwater Technology. In: Proceedings of the 2002 International Symposium on, 2002, pp. 81–86, http://dx.doi.org/10. 1109/UT.2002.1002393.
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Anastasopoulos, I., Gerolymos, N., Drosos, V., Kourkoulis, R., Georgarakos, T., Gazetas, G., 2007. Nonlinear response of deep immersed tunnel to strong seismic shaking. J. Geotechn. Geoenviron. Eng. 133 (9), 1067–1090. http://dx. doi.org/10.1061/(ASCE)1090-0241(2007) 133:9(1067). CCCCHZMB, 2011. Tunnel Design Solution [Format: Images].